| Two-way interaction in latent variables has been a topic of considerable theoretical and practical interest among psychological methodologists. Since the seminal work of Kenny and Judd (1984), much research has focused on the use of product indicators for the estimation of latent moderation effects. These methods are usually difficult to use, and many popular approaches lack solid statistical justification. In recent years, the development of full-information maximum likelihood for nonlinear latent variables models provided a new approach to the estimation of latent variable interaction effects. However, a particular kind of three-way interaction, i.e., two-way latent variable interactions over an observed grouping variable, has received little attention. In this thesis, existing literature is reviewed and studied to arrive at a derivation of the full-information maximum likelihood estimator for three-way interactions in latent variables. It is also shown that this new method of estimation and testing can be implemented in Mplus (Muthen & Muthen, 1998--2007) using mixture modelling. To study the properties of this new estimation method, a simulation study is conducted, and the new method is shown to have superior performance than an existing method proposed by Marsh, Wen, and Hau (2004). |
